A global estimator unbiased by local changes.

The global activity is an important confound when analyzing PET data in that its inclusion in the statistical model can substantially reduce error variance and increase sensitivity. However, by defining global activity as the average over all voxels one introduces a bias that is collinear with experimental factors. This leads to an underestimation of true activations and the introduction of artefactual deactivations. We propose a novel estimator for the global activity based on the notion of finding a maximally nonlocal mode in a multivariate characterization of the data, while maximizing the locality of the remaining modes. The approach uses singular value decomposition (SVD) to find a provisional set of modes, which are subsequently rotated such that a metric based on the above heuristic is maximized. This metric is a version of the stochastic sign change (SSC) criterion that has been used previously for normalizing medical images with focal defects. The estimator was evaluated on simulated and real functional imaging (PET) data. The simulations show that the bias of the global mean, introduced by focal activations, is reduced by 80--90% with the new estimator. Comparison with a previous unbiased estimator, using the empirical data, yielded similar results. The advantage of the new estimator is that it is not informed of experimental design and relies only on general assumptions regarding the nature of the signal.